A Fast Algorithm for k-Memory Messaging Scheme Design in Dynamic Environments with Uncertainty

Zhikang Fan, Weiran Shen

Keywords: K-memory, Information design, Uncertainty

Abstract:

We study the problem of designing the optimal k-memory messaging scheme in a dynamic environment. Specifically, a sender, who can perfectly observe the state of a dynamic environment but cannot take actions, aims to persuade an uninformed, far-sighted receiver to take actions to maximize the long-term utility of the sender, by sending messages. After receiving a message, the self-interested receiver derives a posterior belief and takes an action. The immediate reward of each player can be unaligned, thus the sender needs to ensure persuasiveness when designing the messaging scheme.

We formulate this problem as a bi-linear program and show that there exist infinitely many non-trivial persuasive messaging schemes for any problem instance. Moreover, we show that when the sender uses a k-memory messaging scheme, the optimal strategy for the receiver is also a k-memory strategy. We propose a fast heuristic algorithm for this problem and show that it can be extended to the setting where the sender has threat ability. We experimentally evaluate our algorithm, comparing it with the solution obtained by the Gurobi solver, in terms of performance and running time. Extensive experimental results show that our algorithm outperforms the solution in terms of running time, yet achieves comparable performance.

Category: Long

Student: Graduate

Submission Number: 172